As crews cleared downed trees in and around Milwaukee, some of the worst damage in the state appeared to be in Dane and Grant counties.

In Dane County, a tornado appears to be to blame, the National Weather Service said. With part of a school in Verona collapsed and roofs blown off homes, the county declared a state of emergency Tuesday morning.

Another tornado may have touched down overnight in Grant County, where the City of Platteville also declared a state of emergency. Reports of damage there include flipped cars, power failures and street closings, according to the National Weather Service's LaCrosse office.

Pioneer Stadium and three residence halls -- Bridgeway Commons, Rountree Commons and Southwest Hall -- sustained significant damage at the University of Wisconsin-Platteville, according to a university spokesman.

The university posted photos on its Facebook page showing windows blown out at Engineering Hall and twisted metal bleachers at Pioneer Stadium.

The campus was closed to the public Tuesday, with summer classes canceled for the day and all non-essential employees told to stay home.

Platteville officials are encouraging all residents to stay home as crews work to assess the damage and clear debris.

Some injuries have been reported and as many as a dozen homes may have sustained extensive damage. The city has restricted traffic in its southwest area, which was hit hardest by the storm.

Alliant Energy and Scenic Rivers have shut down power citywide while they assess damages in the area, according to a release from city officials.

Similar efforts are underway in Dane County.

"We believe it was at this point a tornado may have first touched down in the Mineral Point area, lifted and touched down multiple times between New Glarus and Verona," the National Weather Service said.

Dane County Emergency Management officials received about 350 reports of storm damage after the storm packing dangerously high winds hit shortly after midnight. About 15 homes in the City of Verona sustained severe damage, and several power failures were reported, according to officials. Winds were reported to be upward of 60 mph.

Emergency managers said the north side of Verona and the southwest side of Madison suffered the brunt of the damage.

Dawn Sanderson, a Friar Lane resident on Madison's southwest side, told the Wisconsin State Journal that she did not anticipate the extent of the storm, which caused extensive damage to her property.

She detailed the scene she saw upon coming out of safety Tuesday morning: "Flooding, my roof is gone. My garage is gone. Backyard is gone. The trees are gone. Damage (and) water everywhere."

The Salvation Army set up a shelter at Memorial Baptist Church in Verona for displaced residents.

Country View Elementary School in Verona partially collapsed, according to police Lt. David Dresser. The department will take an inventory of damaged homes and other structures later Tuesday.

There were reports of more than 20 homes damaged on Madison's west side as the storms moved through just after midnight.

The Wisconsin State Journal reported that 23 homes were damaged, six with their roofs torn off, in the area surrounding Yorkshire Road and Friar Lane on the west side.

As of Tuesday morning, Madison Gas and Electric was reporting 40 separate failures affecting more than 3,400 customers.

Most of the damage was caused by strong winds and lightning, according to the utility.

Early Tuesday, Madison Mayor Paul Soglin surveyed the damage at homes on the state capital's southwest side.There were reports of trees down in Waukesha and Walworth counties and winds up to 50 mph were reported at Mitchell International.

In Milwaukee, Department of Public Works' officials reported straight-line winds gusting to 50 miles per hour and heavy downpours.

Crews from the city's forestry department were called to work at 3 a.m. and the city had received 70 calls for service as of 8:30 a.m.

The area of North 35th Street and West State Street, east to the lake and as far south as Layton Avenue, sustained the most damage, and calls for service to the city continue to come in, city officials said.

Lt. Schuyler Belott, director of community relations for the Milwaukee Fire Department, said most of the department's morning runs were for reports of wires down.

Power failures in this type of weather are not uncommon in older areas of the city, he said, but no significant damage had been reported in the city as of early Tuesday morning. Regardless, Belott said anyone who comes across a downed wire should stay away from the site and notify 911 because the wire may be a cable wire or a live power line.

About 7,500 Milwaukee County customers were without power as of 10:45 a.m., said Cathy Schulze, spokesperson with We Energies. Just under 13,000 are without power across southeast Wisconsin, and more than 20,000 customers have had their power restored since midnight.

This year has been one of the latest starts to the tornado season in Wisconsin.

Karen Herzog and Don Walker, both of the Journal Sentinel staff, contributed to this report.